Journal of Operator Theory

Volume 54, Issue 1, Summer 2005 pp. 137-146.

On the maximality of subdiagonal algebras

Authors: Quanhua Xu
Author institution: Laboratoire de Math\'{e}matiques, Universit\'{e} de Franche-Comt\'{e}, 25030 Besan\c con, Cedex, France

Summary: We consider Arveson's problem on the maximality of subdiagonal algebras. We prove that a subdiagonal algebra is maximal if it is invariant under the modular group of a faithful normal state which is preserved by the conditional expectation associated with the subdiagonal algebra.

Keywords: Subdiagonal algebra, maximality, modular group, conditional expectation.

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